Quantum communications typically involves transmission of photons in unknown quantum states. Information may be encoded and transmitted in an optical fiber as a transmission channel in either a single-photon state or a two-photon state. One problem typically encountered during transmission is that photons are lost in the optical fiber. Even if a nearly perfect transmitter is employed that emits a perfect single-photon state or a two-photon state each time, the number of photons that make it through the optical fiber transmission channel drops exponentially with distance travelled through the transmission channel. As a result, a major challenge in quantum communications (QC) is that transmission loss exponentially reduces the throughput.
In classical communications, this exponential reduction in throughput does not occur because a classical signal, which generally contains a large number of average photons per bit, may be optically amplified at intermediate points in the transmission line to a degree that information bits are detectable with low probability of error at the receiver. When a signal comprising photons in unknown quantum states is amplified, enough noise is added such that the quality of the unknown state is degraded typically to the point of making it unusable for quantum communications protocols. This amplification of unknown quantum states, often called quantum cloning, necessarily causes a reduction in state quality. In the best case, quantum bit fidelity is reduced from 1 to ⅚ as described in V. Scarani, S. Iblisdir, N. Gisin, and A. Acin, “Quantum Cloning,” Rev. Mod. Phys. 77, 1225 (2005). As a result, many quantum communications applications, such as Quantum Key Distribution (QKD), have generally been considered to be either impossible or impractical when quantum states are transmitted through amplifiers.
A single-photon signal prepared and transmitted in an unknown state cannot be measured and then, based on the measurement outcome, be recreated in exactly the same state. This condition is true because of the no-cloning theorem. As used herein, the no-cloning theorem refers to a condition in which an unknown quantum state cannot be copied without introducing a certain amount of fundamental noise. If a third party attempts to “steal” a photon, copy it, send on the copy to another location, errors in transmission of the photons are necessarily introduced. As a result, the presence of such errors indicate that the transmitted photons are no longer suitable for information use in some quantum communication protocols, such as quantum key distribution (QKD), and can trigger the protocol to be aborted.
As a consequence of the no-cloning theorem, one may create and distribute random keys among users, with a protocol known as quantum key distribution (QKD). QKD typically requires transmission of single-photon level signals in a randomly selected state, so that an ensemble of such states appears random. One way this is achieved is by distributing entangled two-photon states, as each individual photon in an ideal entangled-photon pair has no definite state in the entangled degree of freedom. Unfortunately, direct transmission of entangled photons is greatly limited by the transmission loss described above. For standard single mode telecommunications fiber, the loss is approximately 0.2 dB/km, limiting the maximum usable fiber quantum communications distance (either defined as the span over which Quantum Key Distribution may be performed or a span over which entanglement may be distributed and still be used to violate a Bell inequality) to lengths of less than about 250 km (corresponding to approximately 50 dB loss). Throughput drops by many orders of magnitude from the system transmit rate. While the throughput drop due to attenuation appears to be a fundamental limitation, there is an additional limitation due to receiver noise, which also limits tolerable losses such that the received signal probability is greater than the detector noise probability, which ultimately limits practical applications to fiber spans less than 250 km (see for example, D. Stucki, N. Walenta, F. Vannel, R. T. Thew, N. Gisin, H. Zbinden, S. Gray, C. R. Towery and S. Ten, High Rate, “Long-Distance Quantum Key Distribution over 250 km of Ultra Low Loss Fibers,” New J. Phys. vol 11: 075003 (2009) and Y. Liu, T-Y Chen, J. Wang, W-Q Cai, X. Wan, L-K Chen, J-H Wang, S-B Liu, H. Liang, L. Yang, C-Z Peng, K. Chen, Z-B Chen, and J-W Pan, “Decoy-State Quantum Key Distribution With Polarized Photons over 200 km,” Optics Express vol. 19, pp. 8587-8594 (2010).
Attempts have been made to find scalable solutions to the fiber optic transmission loss problem by (1) employing trusted relays (see for example, M. Peev et al., “The SECOQC Quantum Key Distribution Network in Vienna,” New J. Phys. vol 11:075001 (2009) and references therein) and (2) employing quantum repeaters (see for example, N. Sangouard et al., “Quantum repeaters based on atomic ensembles and linear optics,” Rev. Mod. Phys. 83, 33-80 (2011) and references therein).
Trusted relays break the optical link into several segments, where optical transmission is terminated at each trusted relay and measured. The classical results of measurements are then used to extend the reach over another optical link. While developed for Quantum Key Distribution applications, trusted relays do not work for general communication of quantum states (such as for example, the transmission of entangled states) because classical measurement at each relay destroys the quantum state and, for example, for a qubit, yields only a single classical bit.
Quantum repeaters are envisioned to distribute entanglement over short links, and then store an entangled photon in a quantum memory until an entangled photon from another link arrives at the same quantum memory. At this point, entanglement swapping is performed to build up entanglement over the two links. When a greater number of links are used, the same entanglement swapping protocol is repeated in multiple stages, allowing entanglement may be shared over a larger distance. In addition to requiring quantum memory for the quantum repeater, each entanglement swapping node requires Bell State analysis, which is typically comprised of single-photon detectors and a two-qubit photonic quantum gate.
Unfortunately, such quantum repeaters are not yet practical, although they are presently a focus of multiple research efforts. However, even if they become successful, quantum repeaters would still be subject to latency problems from the classical communication required as part of the protocol.
In addition, as discussed above, current techniques for transmitting single-photon level signals though optical fibers in unknown quantum states are subject to exponential loss in throughput. To achieve a certain throughput after increasing the fiber transmission distance and necessarily increasing the loss, receivers need to wait increasingly longer periods of time to receive the same total number of photons as would be observed after transmission though shorter, lower loss fibers. That waiting period, because of the non-deterministic transmission of the fiber, is a further cause of latency. For example, if photons are transmitted at a gigabit per second, over a typical 200 km long fiber with total loss of 40 dB, even if all other components were ideal, only about one out of every 10,000 sent would be received, making direct transmission highly inefficient.
Accordingly, what would be desirable, but has not yet been provided, is a method and system for facilitating quantum communications that mitigates propagation loss in waveguide transmission of quantum states without violating the no-cloning theorem.